Piezoelectric crystal apparatus



Feb. 1, 1949. wI P, MASON 2,460,520

PIEZOELECTRIG CRYSTAL ABPARATUS Filed Feb. 9, 194e 2 sheets-'sheet 1 0/P0 TASS/UM TAR TRA TE HEM/HVDRATE CRYSTALS n4 R MASON BV A 7' TOR/VE V FREQUENCY COM$`7I4NT IN K/LOCYCLES PER SECOND X TNT/METERS I W. P. MASON PIEZOELECTRIC CRYSTAL APPARATUS Feb. 1, 1949.

2 Sheets-Sheet 2 Filed Feb. 9, 1946 0 +20 +40 +60 +80 TEMPERATURE /N @68555 CENT/GRADE TEIPERAT ATTORNEY Patented Feb. 1, 1949 UNITED sTATEs PATENT OFFICE 2,460,520 l PIEZOELECTRIC CRYSTAL APPARATUS Warren P. Mason, West Orange, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application February 9, 1946, Serial No. 646,639

2.0 Claims. 1

This invention relates to crystal apparatus and particularly to piezolectric crystal elements comprising di-potassium tartrate hemihydrate (K2C4H4Os-1/2(H2O) Such crystal elements may Lbe used as frequency controlling circuit elements in electric Wave lter systems, oscillation generator systems and amplifier systems. Also, they may be utilized as modulators, or as harmonic producers, or as electromechanical transducers in sonic or supersonic projectors, microphones, pick-up devices and detectors.

One of the objects of this invention is to provide advantageous and useful orientations and modes of motion incrystal elements made from synthetic crystalline di-potassium tartrate hemihydrate.

Another object of this invention is to provide synthetic or artificial crystal elements having' a low or substantially zero temperature coelcient of frequency.

Other objects of this invention are to provide crystal elements comprising di-potassium tartrate hemihydrate that may possess useful characteristics, such as effective piezoelectric constants, minimum coupling of the desired mode of motion to undesired modesv of motion therein, and low or zero temperature coefficients of frequency.

A particular object of this invention is to provide di-potassium tartrate hemihydrate crystal elements having a zero temperature coenlcient of frequency at ordinary room temperatures;

Di-pctassium tartrate hemihydrate is a salt of :dextrotartaric acid having a molecule Which lacks symmetry elements. In its crystalline form', it lachs a center of symmetry and belong to a crystal class which is piezoelectric and which in this instance is the monoclinlc sphenoidal crystal class. By virtue of its chemical structure, diipotassium tartrate hemihydrate will formionic and hydrogen-bondedv crystals offering high piezoelectric constants. In addition the crystalline material affords certain cuts with .low temperature coeilicient of frequency and` withk low coupling to other modes of motion therein and a fairly'hgl.:A Q or low dielectric loss and mechanical dissipa tion.

Crystal elements of suitable orientation cut from crystalline iii-potassium tartrate hemihydrate may be excited in different modes of motion such as the longitudinal length or the longitudinal Width modes of motion, or the face shear mode of motion controlled lmainly by the major face dimensions, or the thickness shear mode of motion controlled mainly by the thickness dimension. Also, low frequencyflexural modes of motion of either the width bending ilexure type or the thickness bending duplex flexure type may be obtained.. These various modes of motion are similar in the general form of their motion to those of similar or corresponding names that are knowny in connection with other crystalline substances such as quartz, Rochelle salt and ammonium dihydrogen phosphate crystals.

It is useful to have a synthetic type of piezoelectric crystal element having a low or zero temperature coeicient of frequency, and having a low or zero coupling to other modes of motion therein. In accordance with this invention, such synthetic type crystal cuts may be provided in the form of tartrate crystals and the tartrate crystals may be suitable cuts taken from crystalline di-potassium tartrate hemihydrate adapted to operate in their major face modes of motion. Crystal elements cut fromm-potassium tartrate hemihydrate may have a low or zero temperature coeicient of frequency, and also may possess advantageous elastic properties whereby the longitudinal mode of-motion therein may be substantiallyv free from coupling or interference with the face shear mode of motion therein, or the face shear mode of motion may be free from coupling with other modes of motion therein.

In accordance with this invention, the crystal elements cut from crystalline cli-potassium tar-` trate hemihydrate may be Z-cut type crystal elements having their major faces perpendicular or nearly perpendicular to the Z or c axis and operating in the longitudinal mode of motion along the longest or length dimension thereof, the length dimension being'inclined at an angle 0 of about 22` to 53 ldegrees with respect to the X axis, or about from 30 to 45 degrees Where the zero temperature coefficient of frequency is desired at ordinary room temperatures. Where the angle 0 is an angle between about 22 and de grees, the piezoelectric coupling is of high value at all such 0 angles and has it maximum value at the 0 angle of about 45 degrees. The temperature at which the zero temperature coeflicient of frequency occurs for the longitudinal length mode of motion varies according to the value of the angle of (s selected, and is at about +161@o centigrade for a 0 angle of about l5 degrees, at about +30 centigrade for 0 angle of about 361/2 degrees, and at values between -i-l/,lD and +30@ centigrade for values of e angles between and 37% degrees. The coupling of the longitudinal length mode of motion to the face shear Inode of motion is small, and at the particular o angle of about 521/2 degrees is zero, as particularly disclosed and claimed in my copending application for Piezoelectric 'crystal apparatus Serial No. 659,468, led April 4, 1946 now Patent Number 2,440,694.

Accordingly, in the case of di-potassium tartrate hemihydrate crystals there are among other useful cuts, special cuts each of which have a Zero temperature coecient of frequency and a relatively high electromechanical coupling ofr the order of 20 to 25 per cent,v and each of which may be advantageously used for example as a circuit element in an electric wave filter, or as fand growth habit f crystal of di-potassium tartrate hemihydrate a frequency modulator' for an oscillation generator. It will be noted that the synthetic tartrate crystal elements provided in accordance with this invention have high electromechanical coupling of the order of to 25 per cent, high reactanceresistance ratios Q at resonance, and a small change in frequency over a wide temperaturerange. These advantageous properties together with the low cost and freedom from supply troubles indicate that these crystal elements may may be used in place of quartz as circuit elements in crystal filters and oscillators. Moreover, since the high electromechanical coupling existing in these crystals allows the circuit frequency to be varied in much larger amounts by a reactance tube, than can be done for the fre' quency of quartz, such tartrate crystal cuts may be advantageously used for frequency modulating an oscillation generator.

The tartrate crystal elements provided in accordance With this invention may be especially useful in lter systems for example. For use in channel filters for example, the electromechanical couplingin these crystal elements is so high that regularchannel widths of about 3600 cycles per second for example may be obtained without the use of auxiliary coils for frequencies as low as`60to r100 kilocycles per second for example. Accordingly, such a crystal channel lter may be produced more cheaply and put into a smaller space than one which is used with bulky and expensive coils and condensers. When such crystallter's are to be paralleled, a terminating network comprising coils and condensers maybe used therewith in order to obtain no paralleling loss; or terminating resistances may be used therewith and the paralleling loss made up for by an added stage of amplification. The tartrate crystal elements in accordance with this inven tion Vhave a low ratio of capacities and accordinglymay be used in wide band lterssuch as for example in program filters where the tartrate type crystal element may be used to control the loss peaks located at some distance from the pass band, while using quartz crystals for the sharpest peaks nearest the pass band. The tartrate crystal elements in accordance with this'invention have high coupling and accordingly may be used to extend the range of crystal filters to lower frequencies than have been obtained in the past.4 For example, voic channels 'down to about 12 kilocycles vper second or less may be obtained using a fiexure mode type tartrate crystal element, the flexure modes being obtained by methods presently used in connection with quartz crystal elements. The tartrate crystal elements in accordance with this invention may also be used for control of frequency modulated oscillators. On account of the large electromechanical coupling, the frequency variation and shift may be made of large value and may be controlled may be crystallized, and also illustrating the relation of the surfaces of the mother crystal with respect to the mutually perpendicular X, Y and Z axes, and the crystallographic a, b and c axes; Fig. 2 is an edge View of Fig. l illustrating the y rectangular X, Y and Z and the crystallographic a, b and c systems of axes for monoclinic crystals, and also illustrating the plane of the optic axes of di-potassium tartrate hemihydrate crystals;

Figs. 3 and 4 are perspective views illustrating longitudinal-mode Z-cut type di-potassium tartrate hemihydrate crystal elements rotated in effect about the YZ or c axis toa position corre-f4 sponding to angles of 0=about45 vand 371/2 degrees, respectively; or more broadly 0 angles from 22 to 53 degrees with respect to theX-axis;

Figs. 5 and 6 are graphs illustrating the characteristics of a degree Z-cut type di-potas sium tartrate hemihydrate crystal element;

Figs. 7 and 8 are graphs illustrating the characteristics of a 371/2 degree Z-cut type di-potas-i sium tartrate hemihydrate crystal element;

Fig. 9 is a graph illustrating the characteristics,

of longitudinal-mode Z-cut type di-potassium tartrate hemihydrate crystal elements having angles of 0 from about 22 to 53 degrees;

Fig. 1I) is a graph illustrating the ratio of .capacities of di-potassium tartrate hemihydrate crystal elements as a function of temperature..

This specification follows the conventional terminology, as applied to piezoelectric crystalline substances, which employs a system of three mutually perpendicular X, Y andl Z axes used as reference axes for defining the angular orientation of a crystal element. As used in this specification and as shown in the drawing, the Z axis corresponds to the c axis, the Y axis corresponds to the b axis, and the X axis is inclined at an angle with respect to the a axis which, in the 'case of di-potassium tartrate hemihydrate, is a small angle of about 51 minutes as illustrated in Figs. 1 and 2. The a, b and c axes represent conventional terminology as used by crystallographers.

- Referring to the drawing, Fig. 1 illustrates the general form and growth habit in which dipotassium tartrate hemihydrate may crystallize, the natural faces of the di-potassium tartrate hemihydrate crystal I being designated in Fig. 1 in terms of conventional terminology as used by crystallographers. For example, the top surface of the crystal body I is designated as a 001 plane, and the bottom surface thereof as a 00 1 plane, and other surfaces and facets thereof are as shown in Fig. 1.

yThe mother crystal I, as illustrated in Figyl, may be grown from any suitable saturated nutrient solution by any suitable crystallizer apparatus or method, the nutrient solution used for growing the crystal I being'prepared from any suitable chemical substances and the crystal I being.. grown from such nutrient solution in any crystal' I may be grown to' slze-y by' any'suitable crystallizer` apparatus such as for example by a rocking tank type crystallizer or a reciprocating rotary gyrator type` crystalllzer.

Crystals I comprising di-potassium tartrate hemihydrate (KzClI-I-lOsJ/M-Iehol) form' in the monoclinic sphenoidal class of crystals which has as its element of symmetryk the Yor b crystallographic axis, the Y or b' axis'bein'g an axis ofv binary symmetry. There are four dielectric constants, eight piezoelectric constants and I3 elastic constants involved in such crystalline material. As indicated by the chemical iormula,.di potassium tartrate hemihydrat'e crystals I have 1/ molecule of water of crystallization, as compared to 4 for Rochelle salt crystals. As a result, the water of crystallization is much more tightly bound forcrystals of di-potassium tartrate hemihydrate than for those of Rochelle salt. When held at a temperature ofi about 80 centigrade, there appears to be no observable dehydration of the crystalline di-potassium tartrate hemihydrate; but at some higher temperature of about 150 centigrade the vapor pressure of the crystal reaches atmospheric pressure and will cause bubbling that may 4be observed in an oil bath. If the di-potassium tartrate hemihydrate crystal is placed in a sealed container that is evacuated or lled with dry air, ity will give olf enough moisture to establish its equilibrium vapor pressure, which may be around 10 per cent relative humidity, and it willv be stable from then on. Sudden changes of temperature will not appreciably affect the crystal I since the stable relative humidity at ordinary room temperature is so low.

Di-potassium tartrate hemihydrate crystals I have three cleavage planes which lie along. the three planes determined by the three crystallographlc axes a, b and c. While such cleavage planes may make the crystals I somewhat more diflicult to cut and process, nevertheless satisfactory processing may -be done by using any suitable means such as a sanding belt cooled by oil or by a solution of Water and ethylene glycol, for example.

As illustrated in Fig. 1, monoclinic crystals I comprising di-potassium tartrate hemihydrate are characterized by having two crystallographic axes b and "'c, which are disposed at right angles with respect to each other, and a third crystallographic axis a which makes an angle different than 90 degrees from the other two crystallographic axes b and c. The c axis liesalong the longest direction of the unit cell of the crystalline material. The b axis is an axis of two-fold or binary symmetry. In dealing with the axes and the properties of such a monocllnic crystal I, it is convenient and simpler to use a right-angled or mutually perpendicular system of` X, Y and Z coordinates. Accordingly, as illustrated in Fig. 1

the methodIchosen for relating the conventional right-angled X, Y and Z systemA of axes to the a, bf: and cl system of crystallographic axes. of the crystallographer, is.; to make the Z axiscoincide with-:the c axis-and the Y axis coincide with the b axis, -and to have the X axis lie in the plane of the a and @crystallographic axes atan angle-with respect to the a axis, the X-axis anglebeing about 51 minutes above the a axis for crystalline dipotassiumk tartrate hemihydrate, as shownA in- Fig. 1. The X, Y and Z axes form a mutually perpendicular system of axes, theb or Y axis being a polar axis which is positive (-1-) byv a tension at one of its ends, asl shown in Fig. 1. In order to specify which end' of the Y axis is the positive end, theplane of the two optic axes of the crystal I may bel located. A monoclinic crystal I is an optically biaxial crystal andA for crystalline dipotassiurn tartrate hemihydrate the plane that contains thesev optic axes is found to be parallel to the b or Y crystallographic axis and inclined at an angle'of about 21 degrees with respect to the Z-axis, as illustratedy in Fig. 2.

Fig. 2 is a diagram illustrating the plane of the-optic axes for crystals I comprising di-potassium tartrate hemihydrate. As shown in Fig; 2, the plane ofthe optic axes of a di-potassium tartrate hemihydrate crystal I is parallel to the Y or b axis, which in Fig. 2 is perpendicular to the surface of the drawing; and is inclined in a clockwise direction at an angle of about 2l degrees from the -i-c or -i-Z crystallographic axis. Since the -i-X axis lies at a counter-clockwise angle of degrees from'the-l-c or -i-Z axis, andthe +b=+Y axis makes a right angle system of coordinates with the X and Z axes, the system illustrated in Fig; 2 determines the positive directions of all three of theX, Y and Z axes. Hence the positive directions of all three X, Y and' Z axes may bev specied with reference to the plane of the optic axes of the crystal I. A similar optical method of procedure maybe used for orienting andV specifying the direction ci the three mutually perpendicular X, Y and Z axes of other types of monoclinic crystals. Oriented crystal cuts are usually specied in practice lby known X-ray orientation procedures.

Fig. 3 is a perspective View illustrating` a Z-cut crystal element 2 comprising di-potassium tartrate hemihydrate that has been cut from a suitable mother crystal I as shown in Fig. l; The crystal element 2 as shown in Fig. 3 may be made into the forni ci an elongated. plate of substantiallyA rectangular parallelepiped shape having a longest or length dimension L, a breadth or width dimension W, and a thickness or thin dimension T, the directions of the dimenslons L, W and' T` being mutually perpendicular, andv the thin or thickness dimension T being along the Z axis and measured between the opposite parallel major or electrode faces of the crystal element 2. The length dimension L, andi also the width dimension W' of the crystal element 2, may be made of values to suit theV desired length-mode frequency thereof. The'thickness or thin dimension T may be made ofv a value to suit the impedance of the system in which the crystal element 2 may be utilized as a circuit element; and* also it may be made of a suitable value yto avoid nearby spurious modesy of motion which, by proper diniensioning of the thicknessI dimension T relative to the length and width dimensions L and W, may be placed in a location that is relatively remote from the desired Alongitudinal mode of motion along. the lengthV dimension L.

Suitable conductive electrodes 4 and 5 may be I 4provided adjacent the two opposite major or elecable conductive material deposited upon the surface ofthe crystal element. 2 by evaporation in jvacuum or by other suitable process. The elecjtrodesud and 5 may be electrodes wholly or partially covering the major faces of the crystal element 2, and may be provided in divided or nondivided form as already known. Accordingly, it willlbe understood that the crystal elements 2 disclosed in this specification may be provided with conductive electrodes or coatingsll and 5 on 'their faces of any suitable composition, shape, and arrangement, such as those already known yin connection with ammonium dihydrogen phos phate, Rochelle salt or quartz crystals for example; and that they may be mounted and electrically connected by any suitable means, such as for example, by pressurey type clamping pins or by conductivecoaxial supporting spring wires E cemented by conductive cement 'I or glued to the metallic coatings 4 and 5 deposited on the crystal element 2, as already known in connection with quartz,I Rochelle salt and other crystals having similar or corresponding modes of motion.

' As illustrated in Fig. 3, the crystal element 2 has its major faces disposed perpendicular or nearly perpendicular to the Z or c axis and has its longest or length dimension L inclined at an angle 6 with respect to the -i-X axis, where 0 may be an angle of about 45 degrees or more broadly from 22 to 53 degrees with respect to the -l-X or --a axes, the X axis in the case of di-potassium tartrate hemihydrate being disposed very near tol the a. Iaxis. At the angle of `0,:about 45 degrees with respect to the -l-X axis as particularly illustrated'in Fig. 3, rthe crystal element 2 has its maximum lpiezoelectric coupling, and also has a zero temperature coeicient at about +16.1/2 centigrade for its longitudinal mode of motion along the length dimension L, and at that 0 angle the mechanical coupling of rthat longitudinal mode of motion to the face shear mode of motion therein is not large. At angles of 0 above and below about 45 degrees, the piezoelectric coupling is of somewhat reduced but still effective values, the mechanical coupling of the longitudinal length L mode of motion to the face shear and other modes of motion therein is small, and the position of the temperature at which the zero temperature coefficient of frequency occurs for the longitudinal length L mode of motion is raised or lowered from about +161/2 centigrade, according to the angle of 0 selected, as indicated in Fig. 9.

It will be noted that the natural top and bottom surfaces 001 and 00.1` of the mother crystal l of Fig. 1 extend in fthe plane of the a. and b axes which plane consequently has a normal which makes an angle of about 51 minutesfrom the Z or c axis, as illustrated in Figs. 1 and 2. For practical purposes and ease in processing, the major faces of the crystal element 2 may follow the natural plane surface of the a and b axes of the mother crystal l, in which case they will not be quite perpendicular to the Z and c axes, by the angle of about 51 minutes. The properties of the crystal element I do not vary much with such a small change in the orientation angle.

Accordingly, the crystal. element 2 of'Fig. 3 may haveits major faces nearly perpendicular to the AZ axis and in the plane Aformed by the crystallographic axes aand b.

Asparticularly illustrated in Fig. 3, the length or longest dimension L of the major faces' of the crystal element 2 lies substantially in the plane of the X and Y axes and is inclined at an angle of about 45 degrees with respect to the X and Y axes.,- 'lhe width dimension W of the major faces of the crystal element 2 being perpendicular to the length dimension L thereof will also make an angle of about 45 -degrees with respect to the X and Yaxes. The thickness dimension T extends lalonglor nearly along the Z or c axis. The electrode's 4 and 5 disposed adjacent the major faces of the crystal element 2 provide an electric iield inthe vdirection of the thickness dimension T of the crystal element 2 thereby producing a useful longitudinal mode of motion along the Vlength dimension L of the crystal element 2 with high electromechanical coupling and a'low temperature coefficient Aof frequency over a `temperature range in the region above and below about HG1/2 centigrade.

YThe dimensional ratio of the width dimension W with resepect to the length'dimension L of the crystal eleinent'Z may be made of any suitable value in the region less than 0.7 for example and as particularly described herein may be about 0.5" for longitudinal length mode crystal elements2. The smaller values of dimensional ratios of the width W with respect to the length L, as of the order of 0.5 more or less, have the effect of spacing the width W mode of motion at a frequency which it remote from the funda mental longitudinal mode of motion along the the length Ydimension L thereof, the nodal line occurs-at the center of and transverse to the length dimension L of the crystal element 2 about midway between the opposite small ends thereof and the crystal element 2 may be there mounted and electrically connected by ,any suitable means such as by wires 6 cemented by a spot 'i of conductive cement to the metallic coatings fs' and 5 in the nodal region vof the crystal element 2.

l While the crystal element 2 is particularly described hereinas being operated .in the fundamental longitudinal modeV of motion along its length dimension L, it will be understood that it may be operated in any even or odd order harmonic `thereof in a known manner by means of a plurality of pairs of opposite interconnected electrodes spaced along the length' L thereof. Also, if desired, the crystal element 2 may be operated simultaneously in the -longitudinal length L and width W modes of motion by arrangements as disclosed for example in W. P. Mason Patent No. 2,292,885 dated August 1l, 1942; or simultaneously in the longitudinal length L mode of motion andthe width W fiexure mode of motion by `arrangements as disclosed for example in W. P.Mason Patent No. 2,292,886 dated August 111, 1942 Fig. 4 is a perspective View illustrating a 371/2- degreel z-cutdtpotassium tartlate hemihydrate crystal elementgZ which has 'been cut from a mother crystal l such as that illustrated in Fig. 1.v vThe orientation of the 37'1/2-degree Z-cut crystal element 2 illustrated in Fig. 4 'is similar to thatoi the' '45degree Z-cut crystal element 2 illustrated in Fig. 3, except for the position `of the longest or length dimension L thereof, which in the case of the 371/2-degree Z-cut crystal element 2 of Fig. 4 is inclined at an angle @of about 371/2 degrees with respect to the -l-X axis, instead of :45 degrees, as in the case yof the l15degree Z-cut crystal .element of Fig. 3.

The 371/2-degree Z-.cut crystal element 2 of Fig. 4With its length dimension L disposed at substantially 371/2 degrees vfrom the -l-X axis gives a longitudinal length mode resonant frequency which has a zero temperature coefficient at about +30 centigrade, instead of at about +16,1/2 centigrade as in the case of the 0=45degree Z-cut crystal-element of degree Z-cut crystal element of Fig. 4 may be preferred for use where the ambient temperature is in the region of |30D centigrade. The crystal element 2 of Fig. 4, like the crystal element of Fig. 3, has its major faces disposedperpendicw lar or nearly perpendicular to the Z or c axis; but its length or longest dimension Lis inclined at an angle of tal-:about 371/2 degrees with respect to the -lX or -l-a axis, as illustrated in Fig.'4. The thickness dimension T extends along or nearly along the Z or c axis. The electrodes Itand 5 disposed adjacent the -rnajor faces of the crystal element 2 providean electric field in the general direction .of the thickness `dimension T of the crystal element 2, Ithereby producing a useful longitudinal fmode of motion along the length dimension L of the crystal element 2 with a high electro-mechanical coupling `and a low temperature coefficient of frequencyover an ordinary room temperature range in the region f above and .below +30 centigrade.

Fig. 5 is a graph Iillustrating an example oi the frequency spectrum of l5-degree Z-cut -dipotassium tartrate hemihydrate crystal elements 2 of Fig. 3 having various dimensional ratios of the width W with respect to the length L Within the range between about 0.15 and 0.65. As shown in Fig. 5, the main mode of motion, which is the fundamental longitudinal mode of vibrationalong the length dimension L, is represented by ,the curve labeled A in Fig. 5, and has a frequency constant which varies from about 177 to 169 kilocycles'per secondper centimeter of the length dimension L, depending Vupon -the dimensional ratio of width W to length L selected. Thus, as an example, a l5-degree Z-cut crystalelement 2 having a length dimension L of one centimeter and a dimensional ratio of width Wto length L of about 0.5 will vhave a frequency of about 172 kilocycles per second for its fundamental longitudinal mode of motion along the length dimension L. `A'similar'i5-degree Z-cut crystalelement,but,having a length dimensionL of .another value, will have ra corresponding frequency which varies inversely as .the value of its length dimension L.

The-curve B in Fig. 5 represents a nearby face shear mode of motion which has'a slight coupling to the length longitudinal mode `of motion represented by the curve A. At-,a dimensional ratio of widthW to 1ength;L of aroundfl for example, the main length longitudinal mode of motion representedby the curveAghasa vratio of capacities'around '19.5 to 20, While the face shearmode of motion represented by the curve B-has'a'ratio ofcapacities .of around l500 to 700, as .indicated bythenumerals alongside the curve -Bin Fig. 5. Hence, the effect vof the .secondary face :shear mode .of motion.represented:by the vcurve;Raon the main length longitudinal :mode `of motion -,repre- Fig. 3. Accordingly, the 371/2' shown .in Fig. 7, the main 10 sented by the curve A, is comparatively negligible.

The higher frequency modes of motion shown by the upper set of curves in Fig. .5 are related -to the width longitudinal mode of motion, the main fundamental longitudinal mode of motion along the width dimension W being represented by the curve C in Fig. 5. All of these higher frequency resonances which are related to the width mode of motion represented by the curve C, are, for a li5-degree Z-cut crystal element 2 having a width dimension W equal to about one-half of its length dimension L, disposed above 4twice as high in frequency as the frequency of the main longitudinal Inode of motion represented by the curve A, and do not produce any troublesome interference therewith.

Fig. 6 is a graph illustrating an example of the small variation in the resonant and antiresonant frequencies fr and fa with varying temperatures from -60 to +80 centigrade, in a Li5-degree Z- cut (li-potassium tartrate hemihydrate crystal element 2 of Fig. 3, the crystal element2 having a length dimension L of about 20.14 millimeters, a width dimension W of about 10.175 millimeters, the Width W to length L ratio thus being about 0.5, and having a thickness dimension T of about 0.88 millimeter. As illustrated in Fig.6, the variation in the .antiresonant frequency is given by the curve labeled fa, and the .variation in the resonant frequency is given by -the-curve labeled fr. As shown by lthe-curve fr in Fig. 6, the resonant frequencyjr has a zero temperature coefficient at about +1615 vcentigrade, and from about 0 to +40 centigrade the total variation infre- '1 quency is of the order of about 0.029 per cent,

which isa sufficiently low temperature coeiiicient of frequency to be suitable for use in electric wave crystal lters andin other crystal systems.

The longitudinally clamped dielectric constant of all Z-cut type di-potassium tartrate 4hemihydrate crystals 2 .over a temperature range `from to +100 .centigrade is of .the order of 6.0 expressed in centimeter-gram-seconds units.

Fig. 7 is a graph illustrating an example ofthe frequency spectrum of 371/2-degree Z-cut di-po tassium tartrate hemihydrate crystal elements .f2 of Fig. 4, for various dimensional ratios ofthe width Wvwith respect to the length L within the dimensional range about -fromf0.15 'to 0.65. As mode of motion, which is the fundamental longitudinal or extensional mode of vibration along the length dimension L, is represented by the curve labeled A' in Fig. 7, and has a frequency constant which varies from about 182 to 170 kilocycles per second per centimeter of the length dimension L, dependingupon the selected dimensional ratio of the width W With-respect'to the length L. Thus, as an illustrative example, a 371/2-degree Z-cut crystal element 2 having a length dimension L vof one centimeter and a dimensional ratio of width W' to lengthL of Vabout 0.5 will have a frequency of about 174 kilocycles per second for its fundamental longitudinal mode of motion along the length .dimension L. It will be .understood'that the frequency varies inversely as the length dimension L in a length longitudinal mode crystal element.

The curve B in Fig. 7 represents a-face 4shear mode of motion which has a slight coupling to-the main length longitudinal mode of motion Arepresented :by the curve A in Fig. 7. At the dimensionalratio of width vW to length L around 0.5 for .-exarnple, the main .length longitudinal mode of motion -represented `by the curve A' has. a ratio of capacities around y19.0 as indicated by the fig-v ure 19.0 placed alongside the curve A', while the face shear mode of motion represented by the curve B' has a ratio of capacities of about 36 as indicated by the figure 736pla`ced alongside the curve B' in Fig. 7. Hence the effect of the face shear mode of motion represented by the curve B on the main longitudinal length L mode of motion represented by the curve A' is comparatively negligible.

The higher frequency modes of motion shown bythe upper set of three curves in lFig. 7 are related to the width longitudinal mode of motion,

the main fundamental longitudinal mode of motion along the width dimension W of the 371/2- degree Z-cut crystal element 2 being represented by the curve C' in Fig. 7. All three of these higher frequency resonances related to the curve C4 are, for a 371/2-degree Z-cut crystal element having a width dimension W equal to about onehalf of its length. dimension L, disposed about twice as high in frequency as the frequency of the main longitudinal length mode of motion represented by the curve A', and do not produce any troublesome interference therewith. The numbers appearing adjacent the curves A' and B' in Fig. 7 indicate the approximate values of the ratio of capacity at regions on the curves A and B adjacent the numbers.

Fig. 8 is a graph illustrating an example of the small variation in the resonant and antiresonant frequencies, with change in temperature from -80 to +80 centigrade, for' a 371/2-degree Z-V cut dipotassium tartrate crystal element 2 of Fig. 4, the crystal element having alength dimen# vsion L of about 20.36 millimeters, a width dimension W of about 10.14 millimeters, the width W to length L dimensional ratio thus b eing'about 0.5, and having a thickness dimension T of about 0.9 millimeter. The variation in the anti-resonant frequency is given by the curve labeled fa in Fig. 8, and the variation in the resonant frequency is given by the curve labeled fr. As shown in Fig. 8 by the curve fr, the resonant frequency has a zero temperature coefficient at about'+30 centigrade and over the range from to +60 centigrade the total variation in frequency is small, the frequency remaining constant to about 50 cycles per second out of 100 kilocycles per second. n

Fig. 9 is a graph showing a p lot of the 0 angle of rotation of the length dimension L measured from the X-axis against the temperature for the zero temperature coeflicient of frequency, for Z-cut longitudinal length mode di-potassium tartrate hemihydrate crystal elements 2 of Figs; 3 or 4, when rotated inY effect about the Z axis, the dimensional ratio of width W to length L being about 0.5 in all cases. As shown by theV curve D in Fig. 9, the 0=45degree Z-cut crystal element 2 of Fig. 3 has its' zero temperaturefrequency coeiicient at a temperature of about +161/2" centigrade, and the 0:371/2-degree Z-cut crystal element 2 of Fig. 4 has its zero temperature-frequency coefficient at a temperature of about +30 centigrade. Similarly, when v0- 4221/2)v degrees giving a 221/2-degree Z-cut crystal element, the temperature for the zero temperaturefrequency coefficient is at about 45 centigrade, Similarly, for other angles of 0 between 221/2 and 55 degrees, the temperature for the zero temperature-frequency coefficient in Z-cut di-potassium tartrate crystal elements may be obtained from the curve D of Fig. 9. When the ambient temperature is between and +30 centigrade, the corresponding angle 0 may Couven-- iently be a value between about 30 and 46 degrecs, as shown by the curve D in Fig. 9.

Fig. 10 is a graph illustrating the approximate value of the ratio of capacities of the 0:45 and 371/2degree Z-cut length longitudinal mode dipotassium tartrate hemihydrate crystal elements 2 of Figs. 3 and 4, as a function of temperature over a range from -60 to +80 centigrade. At ordinary room temperatures from +20 to +30 centigrade, the ratio of capacities is in the region between 19 and 20 as shown by the curve E in Fig. 10. The term ratio of capacities, as used in this specification, has its usual significance.

It will be noted that among the several cuts illustrated in Figs. 3, 4 and 9 are orientations for which the temperature-frequency coeucient may be zero at a 'specied temperature To, the irequency variation being sufciently small `over ordinary room temperature range to be useful for example, in wideband filter systems. The low temperature coeicient of frequency together with the high electromechanical coupling, the high Q, the ease of procurement and the low cost of production are advantages of interest for use as circuit elements in electrical systems generally.

Although this invention has been described and illustrated in relation to specific arrangements, it is to be understood that it is capable of application in other organizations and is therefore not to be limited to the particular embodiments disclosed.

What is claimed is:

1. Piezoelectric crystal apparatus comprising means including a di-potassium tartrate crystal body for producing a substantially zero temperature coefficient of vibrational frequency within a temperature range substantially from 0 to +40' centigrade, said frequency being determined by a major face dimension axis of said crystal body, said dimension axis being made of a dimensional value corresponding to the value of said frequency, the angular orientation of said crystal body with respect to the mutually perpendicular X, Y and Z axes thereof being a value corresponding to and related to the value of said substantially zero temperature coefficient of frequency, and electric field-producing means for operating said crystal body at said substantially zero temperature coefficient of frequency.

2. Piezoelectric crystal apparatus comprising means including a di-potassium tartrate crystal body for producing a substantially zero temp-erature coefcient of vibrational frequency within a temperature range substantially from 0 to +40 centigrade, said frequency being determined by a major face dimension axis of said crystal body, said dimension axis being made of a dimensional value corresponding to the value of said frequency,` the angular orientation of said crystal body with respect to the mutually perpendicular X, Y and Z axes thereof being a value corresponding to and related to the value of said substantially zero temperature coefcient of frequency, and electric iieldproducing means for operating said crystal bodyl at said substantially zero temperature coefficient of frequency, said major face of said crystal body being disposed substantially parallel to said Y axis of said X, Y and Z axes.

3. Piezoelectric crystal apparatus comprising ture coefficient of vibrational frequency within a temperature range substantially from 0 to crystal body +40 centigrade, said frequency :being :,deter mined 'by 4a major face dimension axis 4of "said crystal body,said dimension axis 'beingvmade of a dimensional value 'correspondingtothe value of said frequency, the angular orientationsof said Vwith respect to the mutually perpendicular.X,'Y andZ axes thereofzbeingza-value corresponding to. and relatedf to ith'e'value roi.v said substantiallyzero temperature coefficient offrequency, and electric field-:producingzmeans for operating said crystal body:at lsaidfsubstantially zero .temperature coeiicient of frequency, said major face iof `said crystal :body :being disposed substantially paralleltofonezof'said X, YqandpZ axes, said one axis Ybeingfsaid Y-axispancl said major face dimension axis vbeing yinclined 'at `one of .the angles between l0 and ,'zdegrees with .respect to another of said X, `YzandZ axes.

4.A Z-'cut type di-potassium tartrate hemihydrate crystal element of low :temperature coeifcientxof `frequency having `its rvmajor ,faces -disposed substantially ,perpendicular to lthe `Z "axis, the lengthwise-axis dimension of vsaid majorv faces beinginclined at one of the angles substantially from +30 :to +46 degrees with respect tothe +`X axis.

5. A Z-cut type :di-potassium tartrate .hemihydrate lcrystal element :of low temperature Acoeicient ,of frequencyhavingits substantially rectangularv major "faces :disposed .substantially perpendicular to the Z axis, the lengthwise I.axis dimension fand longest edges 'of :said major faces being V,inclined at one ofthe `.angles substantially from +37 to +46 degrees with respect 'to the +X axis.

6. A Z-cut'type di-'potassiumitartrate"hemihydrate crystal element of low/'temperature coefcient of frequency having'its substantially .rectangular majorfacesdisposed substantially perpendicular'gtofthe Z `axisythe lengthwise axis :dimension of said majorfaces being inclined at an angleof substantially +371/2 degreesrwithrespect tothe +X axis.

7. .A Z-cut type dipotassium itartrate hemihydrate Ycrystal element of low temperaturecoeiilicient of frequency having its substantially :rectangular major faces disposed :substantially perpendicular to theZ axis, fthe lengthwise :axis -dimension of said majorfaces being'inclined Aatan angle of substantially@ degrees with respectrto the X axis.

8. Crystal apparatus comprising a di-fpotassium vtartrate hemihydrate `crystal lelement of low temperature mutually 'perpendicular Width and length axis dimensions for its major faces, said major faces being substantially perpendicular Yto the Z axis, and said .length axis vdimension kbeing inclined at an angle of substantially 45 vdegrees Vwith respect to the X axis, said width axis dimension being substantially less than lsaid length axis dimension.

9.Crystal apparatus comprising a dif-potassium tartrate hemihydrate crystal-elementioi'low temperature coefficient of frequency havingrmutually perpendicular width and length axis dimensions for its vmajor faces, said 'major faces being v`substantially f perpendicular to the iZ. axis, and said length axis dimension tbeing .inclined at an angle of substantially +371/2 degrees with respect to the +X axis, said width axis dimension being substantially less than said length axis dimension.

10. Piezoelectric crystal apparatus comprising a di-potassium tartrate hemihydrate crystal elecoeiiicient of vfrequency having mentqhavingmajor faces, saidmajor facesbeing` substantially +22 to +53 degrees withrespect to the +:X axisyand means comprising electrodes disposed Iadjacent'said major faces for operating Ysaid crystal element in a longitudinal mode of Lmotion along said lengthwise dimension'of said crystal element, the temperature coefficient of frequency of said crystal element being substantlally zero at a temperature substantially as given bythe curve in Fig. 9 at a point thereon corresponding to the value of said one of said angles.

11. Piezoelectric crystal apparatus 'comprising adi-potassium tartrate hemihydrate crystal element :having substantially rectangular' major faces, vsaid major faces being disposed substantially perpendicular to the Z axis, the length- Wise axis dimension and longest edges of said major faces 'being inclined at one of the angles to +53 degrees with respect to the +X axis, and means comprising l electrodes disposed adjacent said major faces for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension of said crystal element, the ratio of the width axis .dimension of said major faces with respect f to said lengthwise axis dimension thereof being one :of ithe'values less than 0.7, the temperature coefficient of frequency of said crystal element being substantially zero at a temperature substantially as given `by the curve in Fig. 9 at a point'thereoncorresponding to the value of said oneof said angles.

.12. Piezoelectric crystal apparatus comprising a diepotassium tartrate hemihydrate crystal element having major faces, said major faces being Adisposed substantially perpendicular to the Z axis, the lengthwise axis dimension of said major faces being inclined at one of angles from substantially +30 to +46 degrees with. respect to the +'X axis, yandmeans comprising electrodes Idisposed `adjacent said major faces for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension of said crystal element, said crystal element having a substantially zero `temperature coefficient of frequency at a temperature in the range substantiallyfrom +15 to +30 centigrade.

13. Piezoelectric crystal apparatus comprising a di-potassiurn tartrate hernihydrate crystal element having substantially rectangular major faces, said major faces being disposed substan` tiallyiperpendicular to the Z axis, the lengthwise axis `dimension vand longest edges of said major faces :being Iinclined at one of the angles from substantially +30 to +46 degrees with respect to the +X.axis, and means comprising electrodes disposed adjacent said majorfaces for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension of said crystal element, lthe ratio of the width axis dimensionfof'said majorfaces with respect to said lengthwise axis dimension thereof being one of thevalues less .than 0.7,'said crystal element having ra substantially zero temperature coefficient of ffrequencyat .fa-temperature in the range substantially from +15 to +30 centigrade.

14. Piezoelectric crystal apparatus comprising a cli-potassium tartrate hernihydrate crystal element having substantially rectangular major faces, said major faces being disposed substantially perpendicular to the Z axis, the lengthwise sancionan)y axis dimension and longest edges of said major faces being inclined at one of the angles from substantially +37 to +46v degrees with respect to the +X axis, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension of said crystal elementsaid crystal element having a substantially zero temperature coefficient of frequency at a temperature in the range substantially from +15 to +30 centigrade.

15. Piezoelectric crystal apparatus comprising a. di-potassium tartrate hemihydrate crystal element having substantially 4rectangular major faces, said major faces being disposed substantially perpendicular to the Z axis, the lengthwise axis dimension and longest edges of said major faces being inclined at one of the angles from substantially +37 to +46 degrees with respect to the +X axis, and means comprising electrodes disposed adjacent said major faces'for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension of said crystal element, the ratio of the width axis dimension of said major faces with respect to one of the values less than 0.7 said crystal element having a substantially zero temperature coefficient of frequency at a temperature in the range substantially from +15 to +30 centigrade.

16. Piezoelectric crystal apparatus comprising a di-potassium tartrate hemihydrate crystal element having substantially rectangular major faces, said major faces being disposed substantially perpendicular to the Z axis, the lengthwise axis dimension and longest edges of said major faces being inclined at one of the angles from substantially +37 to +46 degrees with respect to the +X axis,v and means comprising electrodes disposed adjacent said major faces for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension of said'crystal element, the ratio of the width axis dimension of said major faces with respect to said lengthwise axis dimension stantially 0.5, said crystal element having a substantially zero temperature coefficient of frequency at a temperature in the range substantially from +15 to +30 centigrade.

17. Crystal apparatus comprising a di-potassium tartrate hemihydrate crystal element, the major faces of said crystal element being substantially perpendicular to the Z axis, the lengthwise axis dimension of said major faces being inclined at an angle of' substantially A45 degrees with respect to the X axis, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension, said crystal element having a substantially zero temperature coeflicient of frequency at a temperature in the region of substantially +16 centigrade.

18. Crystal apparatus comprising a di-potassium tartrate hemihydrate crystal element, the

' major faces of said crystal element being substantially perpendicular to the Z axis, the lengthwise axis dimension of said major faces being inclined at an angle of substantially +371/2 detnereof being sub- 16' grees with respect to the +X axis', and means comprising electrodes disposed adjacent said major faces for operating said crystal element in a longitudinal mode of motion along said lengthwise dimension.

19. Piezoelectric crystal apparatus comprising a 45 degree Z-cut dil-potassium tartrate hemihydrate crystal element vadapted for longitudinal motion along the length axis dimension of its substantially rectangular major faces, said major faces being substantially perpendicular to the Z axis of the three mutually perpendicular X, Y and Z axes thereof, and said length axis dimension being inclined at an angle of substantially 45 degrees with respect to said X axis, the ratio of the width -axis dimension of said major faces with respect to said length axis dimension being a value not greater than substantially 0.6, said length axis dimension being a value corresponding to the frequency for said longitudinal mode of motion, said length axis dimension expressed in centimeters being one of the values substantially from 177 to 169 divided by the value of said frequency expressed in kilocycles per second, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in saidA longitudinal mode of motion, said crystal element having a substantially zero temperature coefficient of frequency at a temperature in the region of substantially +16 centigrade.

20. Piezoelectric crystal apparatus comprising -a +371/2 degree Z-cut di-potassium tartrate hemihydrate crystal element adapted for longitudinal motion along the length axis dimension of its substantially rectangular major faces, said major faces being substantially perpendicular to the Z axis of the three mutually perpendicular X, Y and Z axes thereof, and said length axis dimension being inclined at an angle of substantially +371/2 degrees with respect to said +X axis, the'ratio of the width axis dimension of said major faces with respect to said length axis dimension being a value not greater than substantially 0.6, said length axis dimension being a Value corresponding to the frequency for said longitudinal mode of motion, said length axis dimension expressed in centimeters being one of the values substantially from 182 to 169 divided by thevalue of said frequency expressed in kilocycles per second, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said longitudinal mode of motion.

WARREN P. MASON.

REFERENCES CITED The following references are of record ln the le of this patent:

OTHER REFERENCES Piezoelectricity, by W. C. Cady; first edition, 1946, McGraw-Hill Book Company, Inc., N. Y. 

